Vladimir V. Basov
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department
Asia G. Slutskaya
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department
This article describes the results of a continued research of invertible formal transformation
of two-dimensional autonomous systems of ordinary differential equations in which the unperturbed part
is being formed by random non-singular quasi-homogeneous first order polynomial with weight (1,2).
For the systems with one of canonical form of this polynomial in non-singular part
there were received resonance equations at the obvious form.
Basing on this equations there heave been proved theorems about formal equivalency of systems
and also there were determined all possible structures of generalized normal form
to which any original system can be traced with the help of almost identical change of variables.